These observations suggest that it would be difficult to interpret the
circuit without having a theory about what it does. But what if we did
assume that this circuit performs probabilistic inference? Much work by cognitive scientists
and neuroscientists has used probabilistic inference as a framework
for explaining behavior, which prompted a search for the correlates of
these models in biological signals (see the growing “Bayesian
brain” literature, e.g., [1]}). Given the
explanatory power of these models with respect to behavior, it
may seem reasonable to look for the molecular signatures and
associated “knobs” that correspond to the components of probabilistic
models, including the prior, the likelihood function and the
posterior. There are at least two conceptual difficulties that arise
in this pursuit that can be seen through the analysis of our circuit. First, while inference about (or perception of) the
environment is typically separated from “action” in these
computational models, in our circuit the two are intimately
coupled. As the time-dependent profiles of the circuit show, the closest
thing to a “molecular correlate” of a posterior-like quantity—the
fraction of activated integrators—only comes into being
through action (regulation of a gene expression program such
as \(\textnormal {A-Program}\)  and \(\textnormal {B-Program}\) ). There is no stable quantity that
serves as a correlate of the posterior through time.
